Disparity energy model provides a biologically plausible mechanism for computing disparity maps from stereograms (Ohzawa, DeAngelis and Freeman, 1990; Qian, 1994). A coarse-to-fine version of the model (Menz and Freeman, 2003; Chen and Qian, 2004), which progresses from large to small scales and uses both position-shift and phase-shift receptive fields, solves stereo matching problem well for many stimuli, including slanted surfaces and natural images. However, because it decodes only one disparity for each location, this model, unlike our visual system, cannot represent two overlapping, transparent planes at different depths. We have now extended the original coarse-to-fine model to solve the difficult stereo transparency problem in a biologically plausible manner. The first extension is to decode all possible disparities from population responses of disparity energy units, instead of decoding only the most probable one as the original model does. The second extension is to apply multiplicative excitation from cells with larger receptive fields to those with smaller receptive fields to implement coarse-to-fine computation. In the original model, coarse-to-fine computation is realized by selecting the group of cells whose binocular receptive fields have a range of phase shifts but a fixed position shift that equals the disparity estimated from cells with larger receptive fields. The current, extended model also uses both position-shift and phase-shift receptive fields, but sets the strongest excitation between cells of different scales when the post-synaptic cell's position-shift parameter matches the pre-synaptic cell's preferred disparity. This modification not only eliminates the artificial "selection" step in the original model but also enables maintenance of complete population responses. With population responses covering the whole range of possible disparities, the new model can represent two transparent planes at different depths reliably. We have demonstrated the success of the model via computer simulations.